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William Jackson presented the morning session. Yeap Ban Har presented this in the afternoon.

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- 1. Theoretical Underpinnings of Singapore Math<br />Sheraton San Diego Mission Valley Hotel, San Diego CA<br />SingaporeMath.com<br />Professional Development<br />Please download from www.mathz4kidz.com<br />Yeap Ban-Har, Ph.D.<br />National Institute of Education<br />Nanyang Technological University <br />Singapore<br />banhar.yeap@nie.edu.sg<br />DaQiao Primary School<br />
- 2. Catholic High School (Primary)<br />
- 3. video of dice problem<br />solving problems<br />instructional models<br />overview<br />Bruner’s theory<br />Skemp’s theory<br />Dienes’ theory<br />
- 4. introduction<br />Wellington Primary School<br />
- 5. Task<br />Lesson Study Problem <br />Wellington Primary School<br />Move 3 sticks to make 3 squares.<br />
- 6. Task<br />Move 3 sticks to make 3 squares.<br />
- 7. Task<br />Move 3 sticks to make 3 squares.<br />
- 8. Task<br />Move 3 sticks to make 2 squares.<br />
- 9. Task<br />Move 3 sticks to make 2 squares.<br />
- 10. Task<br />Move 3 sticks to make 2 squares.<br />
- 11. A Problem from Singapore Grade 6 National Test<br />Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. <br />Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. <br />How many sweets did Ken buy?<br />
- 12. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?<br />chocolates<br />sweets<br />Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.<br />12<br />Jim<br />12<br />18<br />12<br />12<br />12<br />12<br />Ken<br />3 parts 12 + 12 + 12 + 12 + 18 = 66<br />1 part 22<br />Half of the sweets Ken bought = 22 + 12 = 34<br />So Ken bought 68 sweets.`<br />
- 13. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. <br /> How many girls wore swimming goggles on that day?<br />A Problem from a Singapore Classroom<br />Fairfield Methodist Primary School<br />
- 14. <ul><li>88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. </li></ul> How many girls wore swimming goggles on that day?<br />
- 15. 88<br />34<br />54<br /><ul><li>88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. </li></ul>How many girls wore swimming goggles on that day?<br />
- 16. 34 – 20 = 14<br />54 – 34 = 20<br />34<br />54<br />
- 17. 3 x 7 = 21<br />21 girls wear goggles.<br />A Curriculum That Helps Average Students Reach High Achievement<br />
- 18. TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />1995<br />2003<br />2007<br />Grade 4<br />Advanced<br />38<br />41<br />38<br />High<br />70<br />74<br />73<br />Intermediate<br />89<br />92<br />91<br />Low<br />96<br />98<br />97<br />North Vista Primary School<br />
- 19. TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />Average<br />Indonesia<br />Thailand<br />Malaysia<br />Singapore<br />Grade 8<br />Advanced<br />2<br />3<br />0<br />40<br />2<br />High<br />15<br />12<br />4<br />70<br />18<br />Intermediate<br />46<br />44<br />14<br />88<br />50<br />Low<br />75<br />66<br />48<br />97<br />82<br />Method Used in Singapore Textbooks<br />
- 20. Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-regulation of learning<br />Attitudes<br />Metacognition<br />Numerical calculation<br />Algebraic manipulation<br />Spatial visualization<br />Data analysis<br />Measurement<br />Use of mathematical tools<br />Estimation<br />Mathematical Problem Solving<br />Reasoning, communication & connections<br />Thinking skills & heuristics<br />Application & modelling<br />Skills<br />Processes<br />Concepts<br />Numerical<br />Algebraic<br />Geometrical<br />Statistical<br />Probabilistic<br />Analytical<br />Mathematics Curriculum Framework<br />
- 21. Every Child Counts<br />
- 22. effective<br />mathematics<br />teaching<br />BinaBangsa School, Indonesia<br />
- 23. Primary Mathematics 1A<br />Pedagogical Principle:<br />Bruner<br />
- 24. Number Bonds<br />PCF Kindergarten TelokBlangah<br />
- 25. Number Bonds<br />PCF Kindergarten TelokBlangah<br />
- 26. Bruner<br />The concrete pictorial abstract approach is used to help the majority of learners to develop strong foundation in mathematics. <br />Division<br />National Institute of Education<br />
- 27. Division<br />Princess Elizabeth Primary School<br />
- 28. Catholic High School (Primary)<br />
- 29. mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />A lesson from Earlybird Kindergarten Mathematics<br />
- 30. mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
- 31. from<br />concrete<br />to<br />pictorial<br />mathz4kidz Learning Centre, Penang, Malaysia<br />
- 32. from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
- 33. mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
- 34. using<br />concrete<br />materials<br />Professional Development in AteneoGrade School, Manila, The Philippines<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
- 35. Primary Mathematics (Standards Edition) 2A<br />Pictorial Before Abstract<br />
- 36. bruner<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
- 37. skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
- 38. Keys Grade School, Manila, The Philippines<br />
- 39. Keys Grade School, Manila, The Philippines<br />
- 40. Skemp<br />Understanding in mathematics <br /> relational<br /> (conceptual) <br /> instrumental <br /> (procedural)<br /> conventional <br />Teaching for conceptual understanding is given emphasis in Singapore Math.<br />Pedagogical Principle:<br />Skemp<br />Primary Mathematics Standards Edition Grade 6<br />
- 41. Fraction Division<br />Primary Mathematics Standards Edition Grade 6<br />
- 42. skemp<br />Scarsdale Middle School New York<br />
- 43. Dienes<br />Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. <br />Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition <br />Primary Mathematics Standards Edition Grade 1<br />
- 44. Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 1<br />
- 45. Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 2<br />
- 46. homework<br />Are you able to see how these tasks are varied according to Dienes’ idea of mathematical variability? <br />
- 47. How is Task 4 different from Task 5?<br />16<br />Primary Mathematics Standards Edition Grade 5<br />
- 48. 16<br />What is the given in Task 5? What is the given in Task 6? Are these different?<br />30<br />Primary Mathematics Standards Edition Grade 5<br />
- 49. Earlybird Kindergarten Mathematics <br />Standards Edition <br />Can you see how Dienes’ idea is used in designing these tasks?<br />diene’s<br />theory<br />of<br />variation<br />
- 50. dienes<br />Princess Elizabeth Primary School, Singapore<br />
- 51. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding<br />
- 52. conclusion<br />PCF Kindergarten PasirRis<br />
- 53. Instructional Models<br /><ul><li> Coaching
- 54. Modeling
- 55. Providing
- 56. Explaning</li></ul>DaQiao Primary School<br />
- 57. “Children are trulythe future of our nation. “<br />Irving Harris<br />
- 58. This presentation is based on part of one of Singapore pre-service mathematics method courses.<br />50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists.<br />The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.<br />
- 59. TEDS-M Elementary Teachers<br />Content Knowledge<br />TEDS-M Elementary Teachers<br />Pedagogical Content Knowledge<br />
- 60. TEDS-M Middle School Teachers<br />Content Knowledge<br />TEDS-M Middle School Teachers<br />Pedagogical Content Knowledge<br />

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